diff -r c35afa9e89e7 -r ef88c0a30f85 lemon/connectivity.h --- a/lemon/connectivity.h Mon Jan 12 23:11:39 2009 +0100 +++ b/lemon/connectivity.h Thu Nov 05 15:48:01 2009 +0100 @@ -32,7 +32,7 @@ #include #include -/// \ingroup connectivity +/// \ingroup graph_properties /// \file /// \brief Connectivity algorithms /// @@ -40,14 +40,18 @@ namespace lemon { - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Check whether the given undirected graph is connected. + /// \brief Check whether an undirected graph is connected. /// - /// Check whether the given undirected graph is connected. - /// \param graph The undirected graph. - /// \return %True when there is path between any two nodes in the graph. + /// This function checks whether the given undirected graph is connected, + /// i.e. there is a path between any two nodes in the graph. + /// + /// \return \c true if the graph is connected. /// \note By definition, the empty graph is connected. + /// + /// \see countConnectedComponents(), connectedComponents() + /// \see stronglyConnected() template bool connected(const Graph& graph) { checkConcept(); @@ -63,16 +67,22 @@ return true; } - /// \ingroup connectivity + /// \ingroup graph_properties /// /// \brief Count the number of connected components of an undirected graph /// - /// Count the number of connected components of an undirected graph + /// This function counts the number of connected components of the given + /// undirected graph. /// - /// \param graph The graph. It must be undirected. - /// \return The number of components + /// The connected components are the classes of an equivalence relation + /// on the nodes of an undirected graph. Two nodes are in the same class + /// if they are connected with a path. + /// + /// \return The number of connected components. /// \note By definition, the empty graph consists /// of zero connected components. + /// + /// \see connected(), connectedComponents() template int countConnectedComponents(const Graph &graph) { checkConcept(); @@ -105,19 +115,30 @@ return compNum; } - /// \ingroup connectivity + /// \ingroup graph_properties /// /// \brief Find the connected components of an undirected graph /// - /// Find the connected components of an undirected graph. + /// This function finds the connected components of the given undirected + /// graph. /// - /// \param graph The graph. It must be undirected. + /// The connected components are the classes of an equivalence relation + /// on the nodes of an undirected graph. Two nodes are in the same class + /// if they are connected with a path. + /// + /// \image html connected_components.png + /// \image latex connected_components.eps "Connected components" width=\textwidth + /// + /// \param graph The undirected graph. /// \retval compMap A writable node map. The values will be set from 0 to - /// the number of the connected components minus one. Each values of the map - /// will be set exactly once, the values of a certain component will be + /// the number of the connected components minus one. Each value of the map + /// will be set exactly once, and the values of a certain component will be /// set continuously. - /// \return The number of components + /// \return The number of connected components. + /// \note By definition, the empty graph consists + /// of zero connected components. /// + /// \see connected(), countConnectedComponents() template int connectedComponents(const Graph &graph, NodeMap &compMap) { checkConcept(); @@ -227,17 +248,19 @@ } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Check whether the given directed graph is strongly connected. + /// \brief Check whether a directed graph is strongly connected. /// - /// Check whether the given directed graph is strongly connected. The - /// graph is strongly connected when any two nodes of the graph are + /// This function checks whether the given directed graph is strongly + /// connected, i.e. any two nodes of the digraph are /// connected with directed paths in both direction. - /// \return %False when the graph is not strongly connected. - /// \see connected /// - /// \note By definition, the empty graph is strongly connected. + /// \return \c true if the digraph is strongly connected. + /// \note By definition, the empty digraph is strongly connected. + /// + /// \see countStronglyConnectedComponents(), stronglyConnectedComponents() + /// \see connected() template bool stronglyConnected(const Digraph& digraph) { checkConcept(); @@ -268,7 +291,7 @@ typedef typename RDigraph::NodeIt RNodeIt; RDigraph rdigraph(digraph); - typedef DfsVisitor RVisitor; + typedef DfsVisitor RVisitor; RVisitor rvisitor; DfsVisit rdfs(rdigraph, rvisitor); @@ -285,20 +308,24 @@ return true; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Count the strongly connected components of a directed graph + /// \brief Count the number of strongly connected components of a + /// directed graph /// - /// Count the strongly connected components of a directed graph. + /// This function counts the number of strongly connected components of + /// the given directed graph. + /// /// The strongly connected components are the classes of an - /// equivalence relation on the nodes of the graph. Two nodes are in + /// equivalence relation on the nodes of a digraph. Two nodes are in /// the same class if they are connected with directed paths in both /// direction. /// - /// \param digraph The graph. - /// \return The number of components - /// \note By definition, the empty graph has zero + /// \return The number of strongly connected components. + /// \note By definition, the empty digraph has zero /// strongly connected components. + /// + /// \see stronglyConnected(), stronglyConnectedComponents() template int countStronglyConnectedComponents(const Digraph& digraph) { checkConcept(); @@ -349,25 +376,33 @@ return compNum; } - /// \ingroup connectivity + /// \ingroup graph_properties /// /// \brief Find the strongly connected components of a directed graph /// - /// Find the strongly connected components of a directed graph. The - /// strongly connected components are the classes of an equivalence - /// relation on the nodes of the graph. Two nodes are in - /// relationship when there are directed paths between them in both - /// direction. In addition, the numbering of components will satisfy - /// that there is no arc going from a higher numbered component to - /// a lower. + /// This function finds the strongly connected components of the given + /// directed graph. In addition, the numbering of the components will + /// satisfy that there is no arc going from a higher numbered component + /// to a lower one (i.e. it provides a topological order of the components). + /// + /// The strongly connected components are the classes of an + /// equivalence relation on the nodes of a digraph. Two nodes are in + /// the same class if they are connected with directed paths in both + /// direction. + /// + /// \image html strongly_connected_components.png + /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth /// /// \param digraph The digraph. /// \retval compMap A writable node map. The values will be set from 0 to /// the number of the strongly connected components minus one. Each value - /// of the map will be set exactly once, the values of a certain component - /// will be set continuously. - /// \return The number of components + /// of the map will be set exactly once, and the values of a certain + /// component will be set continuously. + /// \return The number of strongly connected components. + /// \note By definition, the empty digraph has zero + /// strongly connected components. /// + /// \see stronglyConnected(), countStronglyConnectedComponents() template int stronglyConnectedComponents(const Digraph& digraph, NodeMap& compMap) { checkConcept(); @@ -416,23 +451,28 @@ return compNum; } - /// \ingroup connectivity + /// \ingroup graph_properties /// /// \brief Find the cut arcs of the strongly connected components. /// - /// Find the cut arcs of the strongly connected components. - /// The strongly connected components are the classes of an equivalence - /// relation on the nodes of the graph. Two nodes are in relationship - /// when there are directed paths between them in both direction. + /// This function finds the cut arcs of the strongly connected components + /// of the given digraph. + /// + /// The strongly connected components are the classes of an + /// equivalence relation on the nodes of a digraph. Two nodes are in + /// the same class if they are connected with directed paths in both + /// direction. /// The strongly connected components are separated by the cut arcs. /// - /// \param graph The graph. - /// \retval cutMap A writable node map. The values will be set true when the - /// arc is a cut arc. + /// \param digraph The digraph. + /// \retval cutMap A writable arc map. The values will be set to \c true + /// for the cut arcs (exactly once for each cut arc), and will not be + /// changed for other arcs. + /// \return The number of cut arcs. /// - /// \return The number of cut arcs + /// \see stronglyConnected(), stronglyConnectedComponents() template - int stronglyConnectedCutArcs(const Digraph& graph, ArcMap& cutMap) { + int stronglyConnectedCutArcs(const Digraph& digraph, ArcMap& cutMap) { checkConcept(); typedef typename Digraph::Node Node; typedef typename Digraph::Arc Arc; @@ -444,13 +484,13 @@ typedef std::vector Container; typedef typename Container::iterator Iterator; - Container nodes(countNodes(graph)); + Container nodes(countNodes(digraph)); typedef LeaveOrderVisitor Visitor; Visitor visitor(nodes.begin()); - DfsVisit dfs(graph, visitor); + DfsVisit dfs(digraph, visitor); dfs.init(); - for (NodeIt it(graph); it != INVALID; ++it) { + for (NodeIt it(digraph); it != INVALID; ++it) { if (!dfs.reached(it)) { dfs.addSource(it); dfs.start(); @@ -460,14 +500,14 @@ typedef typename Container::reverse_iterator RIterator; typedef ReverseDigraph RDigraph; - RDigraph rgraph(graph); + RDigraph rdigraph(digraph); int cutNum = 0; typedef StronglyConnectedCutArcsVisitor RVisitor; - RVisitor rvisitor(rgraph, cutMap, cutNum); + RVisitor rvisitor(rdigraph, cutMap, cutNum); - DfsVisit rdfs(rgraph, rvisitor); + DfsVisit rdfs(rdigraph, rvisitor); rdfs.init(); for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { @@ -700,32 +740,37 @@ template int countBiNodeConnectedComponents(const Graph& graph); - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Checks the graph is bi-node-connected. + /// \brief Check whether an undirected graph is bi-node-connected. /// - /// This function checks that the undirected graph is bi-node-connected - /// graph. The graph is bi-node-connected if any two undirected edge is - /// on same circle. + /// This function checks whether the given undirected graph is + /// bi-node-connected, i.e. any two edges are on same circle. /// - /// \param graph The graph. - /// \return %True when the graph bi-node-connected. + /// \return \c true if the graph bi-node-connected. + /// \note By definition, the empty graph is bi-node-connected. + /// + /// \see countBiNodeConnectedComponents(), biNodeConnectedComponents() template bool biNodeConnected(const Graph& graph) { return countBiNodeConnectedComponents(graph) <= 1; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Count the biconnected components. + /// \brief Count the number of bi-node-connected components of an + /// undirected graph. /// - /// This function finds the bi-node-connected components in an undirected - /// graph. The biconnected components are the classes of an equivalence - /// relation on the undirected edges. Two undirected edge is in relationship - /// when they are on same circle. + /// This function counts the number of bi-node-connected components of + /// the given undirected graph. /// - /// \param graph The graph. - /// \return The number of components. + /// The bi-node-connected components are the classes of an equivalence + /// relation on the edges of a undirected graph. Two edges are in the + /// same class if they are on same circle. + /// + /// \return The number of bi-node-connected components. + /// + /// \see biNodeConnected(), biNodeConnectedComponents() template int countBiNodeConnectedComponents(const Graph& graph) { checkConcept(); @@ -750,22 +795,28 @@ return compNum; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Find the bi-node-connected components. + /// \brief Find the bi-node-connected components of an undirected graph. /// - /// This function finds the bi-node-connected components in an undirected - /// graph. The bi-node-connected components are the classes of an equivalence - /// relation on the undirected edges. Two undirected edge are in relationship - /// when they are on same circle. + /// This function finds the bi-node-connected components of the given + /// undirected graph. /// - /// \param graph The graph. - /// \retval compMap A writable uedge map. The values will be set from 0 - /// to the number of the biconnected components minus one. Each values - /// of the map will be set exactly once, the values of a certain component - /// will be set continuously. - /// \return The number of components. + /// The bi-node-connected components are the classes of an equivalence + /// relation on the edges of a undirected graph. Two edges are in the + /// same class if they are on same circle. /// + /// \image html node_biconnected_components.png + /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth + /// + /// \param graph The undirected graph. + /// \retval compMap A writable edge map. The values will be set from 0 + /// to the number of the bi-node-connected components minus one. Each + /// value of the map will be set exactly once, and the values of a + /// certain component will be set continuously. + /// \return The number of bi-node-connected components. + /// + /// \see biNodeConnected(), countBiNodeConnectedComponents() template int biNodeConnectedComponents(const Graph& graph, EdgeMap& compMap) { @@ -793,20 +844,27 @@ return compNum; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Find the bi-node-connected cut nodes. + /// \brief Find the bi-node-connected cut nodes in an undirected graph. /// - /// This function finds the bi-node-connected cut nodes in an undirected - /// graph. The bi-node-connected components are the classes of an equivalence - /// relation on the undirected edges. Two undirected edges are in - /// relationship when they are on same circle. The biconnected components - /// are separted by nodes which are the cut nodes of the components. + /// This function finds the bi-node-connected cut nodes in the given + /// undirected graph. /// - /// \param graph The graph. - /// \retval cutMap A writable edge map. The values will be set true when - /// the node separate two or more components. + /// The bi-node-connected components are the classes of an equivalence + /// relation on the edges of a undirected graph. Two edges are in the + /// same class if they are on same circle. + /// The bi-node-connected components are separted by the cut nodes of + /// the components. + /// + /// \param graph The undirected graph. + /// \retval cutMap A writable node map. The values will be set to + /// \c true for the nodes that separate two or more components + /// (exactly once for each cut node), and will not be changed for + /// other nodes. /// \return The number of the cut nodes. + /// + /// \see biNodeConnected(), biNodeConnectedComponents() template int biNodeConnectedCutNodes(const Graph& graph, NodeMap& cutMap) { checkConcept(); @@ -1023,32 +1081,39 @@ template int countBiEdgeConnectedComponents(const Graph& graph); - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Checks that the graph is bi-edge-connected. + /// \brief Check whether an undirected graph is bi-edge-connected. /// - /// This function checks that the graph is bi-edge-connected. The undirected - /// graph is bi-edge-connected when any two nodes are connected with two - /// edge-disjoint paths. + /// This function checks whether the given undirected graph is + /// bi-edge-connected, i.e. any two nodes are connected with at least + /// two edge-disjoint paths. /// - /// \param graph The undirected graph. - /// \return The number of components. + /// \return \c true if the graph is bi-edge-connected. + /// \note By definition, the empty graph is bi-edge-connected. + /// + /// \see countBiEdgeConnectedComponents(), biEdgeConnectedComponents() template bool biEdgeConnected(const Graph& graph) { return countBiEdgeConnectedComponents(graph) <= 1; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Count the bi-edge-connected components. + /// \brief Count the number of bi-edge-connected components of an + /// undirected graph. /// - /// This function count the bi-edge-connected components in an undirected - /// graph. The bi-edge-connected components are the classes of an equivalence - /// relation on the nodes. Two nodes are in relationship when they are - /// connected with at least two edge-disjoint paths. + /// This function counts the number of bi-edge-connected components of + /// the given undirected graph. /// - /// \param graph The undirected graph. - /// \return The number of components. + /// The bi-edge-connected components are the classes of an equivalence + /// relation on the nodes of an undirected graph. Two nodes are in the + /// same class if they are connected with at least two edge-disjoint + /// paths. + /// + /// \return The number of bi-edge-connected components. + /// + /// \see biEdgeConnected(), biEdgeConnectedComponents() template int countBiEdgeConnectedComponents(const Graph& graph) { checkConcept(); @@ -1073,22 +1138,29 @@ return compNum; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Find the bi-edge-connected components. + /// \brief Find the bi-edge-connected components of an undirected graph. /// - /// This function finds the bi-edge-connected components in an undirected - /// graph. The bi-edge-connected components are the classes of an equivalence - /// relation on the nodes. Two nodes are in relationship when they are - /// connected at least two edge-disjoint paths. + /// This function finds the bi-edge-connected components of the given + /// undirected graph. /// - /// \param graph The graph. + /// The bi-edge-connected components are the classes of an equivalence + /// relation on the nodes of an undirected graph. Two nodes are in the + /// same class if they are connected with at least two edge-disjoint + /// paths. + /// + /// \image html edge_biconnected_components.png + /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth + /// + /// \param graph The undirected graph. /// \retval compMap A writable node map. The values will be set from 0 to - /// the number of the biconnected components minus one. Each values - /// of the map will be set exactly once, the values of a certain component - /// will be set continuously. - /// \return The number of components. + /// the number of the bi-edge-connected components minus one. Each value + /// of the map will be set exactly once, and the values of a certain + /// component will be set continuously. + /// \return The number of bi-edge-connected components. /// + /// \see biEdgeConnected(), countBiEdgeConnectedComponents() template int biEdgeConnectedComponents(const Graph& graph, NodeMap& compMap) { checkConcept(); @@ -1115,21 +1187,27 @@ return compNum; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Find the bi-edge-connected cut edges. + /// \brief Find the bi-edge-connected cut edges in an undirected graph. /// - /// This function finds the bi-edge-connected components in an undirected - /// graph. The bi-edge-connected components are the classes of an equivalence - /// relation on the nodes. Two nodes are in relationship when they are - /// connected with at least two edge-disjoint paths. The bi-edge-connected - /// components are separted by edges which are the cut edges of the - /// components. + /// This function finds the bi-edge-connected cut edges in the given + /// undirected graph. /// - /// \param graph The graph. - /// \retval cutMap A writable node map. The values will be set true when the - /// edge is a cut edge. + /// The bi-edge-connected components are the classes of an equivalence + /// relation on the nodes of an undirected graph. Two nodes are in the + /// same class if they are connected with at least two edge-disjoint + /// paths. + /// The bi-edge-connected components are separted by the cut edges of + /// the components. + /// + /// \param graph The undirected graph. + /// \retval cutMap A writable edge map. The values will be set to \c true + /// for the cut edges (exactly once for each cut edge), and will not be + /// changed for other edges. /// \return The number of cut edges. + /// + /// \see biEdgeConnected(), biEdgeConnectedComponents() template int biEdgeConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { checkConcept(); @@ -1179,21 +1257,64 @@ } - /// \ingroup connectivity + /// \ingroup graph_properties + /// + /// \brief Check whether a digraph is DAG. + /// + /// This function checks whether the given digraph is DAG, i.e. + /// \e Directed \e Acyclic \e Graph. + /// \return \c true if there is no directed cycle in the digraph. + /// \see acyclic() + template + bool dag(const Digraph& digraph) { + + checkConcept(); + + typedef typename Digraph::Node Node; + typedef typename Digraph::NodeIt NodeIt; + typedef typename Digraph::Arc Arc; + + typedef typename Digraph::template NodeMap ProcessedMap; + + typename Dfs::template SetProcessedMap:: + Create dfs(digraph); + + ProcessedMap processed(digraph); + dfs.processedMap(processed); + + dfs.init(); + for (NodeIt it(digraph); it != INVALID; ++it) { + if (!dfs.reached(it)) { + dfs.addSource(it); + while (!dfs.emptyQueue()) { + Arc arc = dfs.nextArc(); + Node target = digraph.target(arc); + if (dfs.reached(target) && !processed[target]) { + return false; + } + dfs.processNextArc(); + } + } + } + return true; + } + + /// \ingroup graph_properties /// /// \brief Sort the nodes of a DAG into topolgical order. /// - /// Sort the nodes of a DAG into topolgical order. + /// This function sorts the nodes of the given acyclic digraph (DAG) + /// into topolgical order. /// - /// \param graph The graph. It must be directed and acyclic. + /// \param digraph The digraph, which must be DAG. /// \retval order A writable node map. The values will be set from 0 to - /// the number of the nodes in the graph minus one. Each values of the map - /// will be set exactly once, the values will be set descending order. + /// the number of the nodes in the digraph minus one. Each value of the + /// map will be set exactly once, and the values will be set descending + /// order. /// - /// \see checkedTopologicalSort - /// \see dag + /// \see dag(), checkedTopologicalSort() template - void topologicalSort(const Digraph& graph, NodeMap& order) { + void topologicalSort(const Digraph& digraph, NodeMap& order) { using namespace _connectivity_bits; checkConcept(); @@ -1204,13 +1325,13 @@ typedef typename Digraph::Arc Arc; TopologicalSortVisitor - visitor(order, countNodes(graph)); + visitor(order, countNodes(digraph)); DfsVisit > - dfs(graph, visitor); + dfs(digraph, visitor); dfs.init(); - for (NodeIt it(graph); it != INVALID; ++it) { + for (NodeIt it(digraph); it != INVALID; ++it) { if (!dfs.reached(it)) { dfs.addSource(it); dfs.start(); @@ -1218,22 +1339,22 @@ } } - /// \ingroup connectivity + /// \ingroup graph_properties /// /// \brief Sort the nodes of a DAG into topolgical order. /// - /// Sort the nodes of a DAG into topolgical order. It also checks - /// that the given graph is DAG. + /// This function sorts the nodes of the given acyclic digraph (DAG) + /// into topolgical order and also checks whether the given digraph + /// is DAG. /// - /// \param digraph The graph. It must be directed and acyclic. - /// \retval order A readable - writable node map. The values will be set - /// from 0 to the number of the nodes in the graph minus one. Each values - /// of the map will be set exactly once, the values will be set descending - /// order. - /// \return %False when the graph is not DAG. + /// \param digraph The digraph. + /// \retval order A readable and writable node map. The values will be + /// set from 0 to the number of the nodes in the digraph minus one. + /// Each value of the map will be set exactly once, and the values will + /// be set descending order. + /// \return \c false if the digraph is not DAG. /// - /// \see topologicalSort - /// \see dag + /// \see dag(), topologicalSort() template bool checkedTopologicalSort(const Digraph& digraph, NodeMap& order) { using namespace _connectivity_bits; @@ -1273,56 +1394,13 @@ return true; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Check that the given directed graph is a DAG. + /// \brief Check whether an undirected graph is acyclic. /// - /// Check that the given directed graph is a DAG. The DAG is - /// an Directed Acyclic Digraph. - /// \return %False when the graph is not DAG. - /// \see acyclic - template - bool dag(const Digraph& digraph) { - - checkConcept(); - - typedef typename Digraph::Node Node; - typedef typename Digraph::NodeIt NodeIt; - typedef typename Digraph::Arc Arc; - - typedef typename Digraph::template NodeMap ProcessedMap; - - typename Dfs::template SetProcessedMap:: - Create dfs(digraph); - - ProcessedMap processed(digraph); - dfs.processedMap(processed); - - dfs.init(); - for (NodeIt it(digraph); it != INVALID; ++it) { - if (!dfs.reached(it)) { - dfs.addSource(it); - while (!dfs.emptyQueue()) { - Arc edge = dfs.nextArc(); - Node target = digraph.target(edge); - if (dfs.reached(target) && !processed[target]) { - return false; - } - dfs.processNextArc(); - } - } - } - return true; - } - - /// \ingroup connectivity - /// - /// \brief Check that the given undirected graph is acyclic. - /// - /// Check that the given undirected graph acyclic. - /// \param graph The undirected graph. - /// \return %True when there is no circle in the graph. - /// \see dag + /// This function checks whether the given undirected graph is acyclic. + /// \return \c true if there is no cycle in the graph. + /// \see dag() template bool acyclic(const Graph& graph) { checkConcept(); @@ -1335,11 +1413,11 @@ if (!dfs.reached(it)) { dfs.addSource(it); while (!dfs.emptyQueue()) { - Arc edge = dfs.nextArc(); - Node source = graph.source(edge); - Node target = graph.target(edge); + Arc arc = dfs.nextArc(); + Node source = graph.source(arc); + Node target = graph.target(arc); if (dfs.reached(target) && - dfs.predArc(source) != graph.oppositeArc(edge)) { + dfs.predArc(source) != graph.oppositeArc(arc)) { return false; } dfs.processNextArc(); @@ -1349,28 +1427,29 @@ return true; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Check that the given undirected graph is tree. + /// \brief Check whether an undirected graph is tree. /// - /// Check that the given undirected graph is tree. - /// \param graph The undirected graph. - /// \return %True when the graph is acyclic and connected. + /// This function checks whether the given undirected graph is tree. + /// \return \c true if the graph is acyclic and connected. + /// \see acyclic(), connected() template bool tree(const Graph& graph) { checkConcept(); typedef typename Graph::Node Node; typedef typename Graph::NodeIt NodeIt; typedef typename Graph::Arc Arc; + if (NodeIt(graph) == INVALID) return true; Dfs dfs(graph); dfs.init(); dfs.addSource(NodeIt(graph)); while (!dfs.emptyQueue()) { - Arc edge = dfs.nextArc(); - Node source = graph.source(edge); - Node target = graph.target(edge); + Arc arc = dfs.nextArc(); + Node source = graph.source(arc); + Node target = graph.target(arc); if (dfs.reached(target) && - dfs.predArc(source) != graph.oppositeArc(edge)) { + dfs.predArc(source) != graph.oppositeArc(arc)) { return false; } dfs.processNextArc(); @@ -1441,17 +1520,16 @@ }; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Check if the given undirected graph is bipartite or not + /// \brief Check whether an undirected graph is bipartite. /// - /// The function checks if the given undirected \c graph graph is bipartite - /// or not. The \ref Bfs algorithm is used to calculate the result. - /// \param graph The undirected graph. - /// \return %True if \c graph is bipartite, %false otherwise. - /// \sa bipartitePartitions + /// The function checks whether the given undirected graph is bipartite. + /// \return \c true if the graph is bipartite. + /// + /// \see bipartitePartitions() template - inline bool bipartite(const Graph &graph){ + bool bipartite(const Graph &graph){ using namespace _connectivity_bits; checkConcept(); @@ -1478,23 +1556,29 @@ return true; } - /// \ingroup connectivity + /// \ingroup graph_properties /// - /// \brief Check if the given undirected graph is bipartite or not + /// \brief Find the bipartite partitions of an undirected graph. /// - /// The function checks if the given undirected graph is bipartite - /// or not. The \ref Bfs algorithm is used to calculate the result. - /// During the execution, the \c partMap will be set as the two - /// partitions of the graph. + /// This function checks whether the given undirected graph is bipartite + /// and gives back the bipartite partitions. + /// + /// \image html bipartite_partitions.png + /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth + /// /// \param graph The undirected graph. - /// \retval partMap A writable bool map of nodes. It will be set as the - /// two partitions of the graph. - /// \return %True if \c graph is bipartite, %false otherwise. + /// \retval partMap A writable node map of \c bool (or convertible) value + /// type. The values will be set to \c true for one component and + /// \c false for the other one. + /// \return \c true if the graph is bipartite, \c false otherwise. + /// + /// \see bipartite() template - inline bool bipartitePartitions(const Graph &graph, NodeMap &partMap){ + bool bipartitePartitions(const Graph &graph, NodeMap &partMap){ using namespace _connectivity_bits; checkConcept(); + checkConcept, NodeMap>(); typedef typename Graph::Node Node; typedef typename Graph::NodeIt NodeIt; @@ -1519,53 +1603,59 @@ return true; } - /// \brief Returns true when there are not loop edges in the graph. + /// \ingroup graph_properties /// - /// Returns true when there are not loop edges in the graph. - template - bool loopFree(const Digraph& digraph) { - for (typename Digraph::ArcIt it(digraph); it != INVALID; ++it) { - if (digraph.source(it) == digraph.target(it)) return false; + /// \brief Check whether the given graph contains no loop arcs/edges. + /// + /// This function returns \c true if there are no loop arcs/edges in + /// the given graph. It works for both directed and undirected graphs. + template + bool loopFree(const Graph& graph) { + for (typename Graph::ArcIt it(graph); it != INVALID; ++it) { + if (graph.source(it) == graph.target(it)) return false; } return true; } - /// \brief Returns true when there are not parallel edges in the graph. + /// \ingroup graph_properties /// - /// Returns true when there are not parallel edges in the graph. - template - bool parallelFree(const Digraph& digraph) { - typename Digraph::template NodeMap reached(digraph, false); - for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) { - for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { - if (reached[digraph.target(a)]) return false; - reached.set(digraph.target(a), true); + /// \brief Check whether the given graph contains no parallel arcs/edges. + /// + /// This function returns \c true if there are no parallel arcs/edges in + /// the given graph. It works for both directed and undirected graphs. + template + bool parallelFree(const Graph& graph) { + typename Graph::template NodeMap reached(graph, 0); + int cnt = 1; + for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { + for (typename Graph::OutArcIt a(graph, n); a != INVALID; ++a) { + if (reached[graph.target(a)] == cnt) return false; + reached[graph.target(a)] = cnt; } - for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { - reached.set(digraph.target(a), false); - } + ++cnt; } return true; } - /// \brief Returns true when there are not loop edges and parallel - /// edges in the graph. + /// \ingroup graph_properties /// - /// Returns true when there are not loop edges and parallel edges in - /// the graph. - template - bool simpleDigraph(const Digraph& digraph) { - typename Digraph::template NodeMap reached(digraph, false); - for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) { - reached.set(n, true); - for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { - if (reached[digraph.target(a)]) return false; - reached.set(digraph.target(a), true); + /// \brief Check whether the given graph is simple. + /// + /// This function returns \c true if the given graph is simple, i.e. + /// it contains no loop arcs/edges and no parallel arcs/edges. + /// The function works for both directed and undirected graphs. + /// \see loopFree(), parallelFree() + template + bool simpleGraph(const Graph& graph) { + typename Graph::template NodeMap reached(graph, 0); + int cnt = 1; + for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { + reached[n] = cnt; + for (typename Graph::OutArcIt a(graph, n); a != INVALID; ++a) { + if (reached[graph.target(a)] == cnt) return false; + reached[graph.target(a)] = cnt; } - for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { - reached.set(digraph.target(a), false); - } - reached.set(n, false); + ++cnt; } return true; }